To solve the equation:

1/3x + 1/4x + 1/8x = 34/45

First, find a common denominator for the fractions on the left side of the equation. The least common denominator for 3, 4, and 8 is 24.

Rewrite the equation with the common denominator:

(8/24)x + (6/24)x + (3/24)x = 34/45

Combine the fractions:

(17/24)x = 34/45

Now, isolate x by multiplying both sides of the equation by (24/17):

x = (34/45) * (24/17)
x = (816/765)
x = 32/30
x = 16/15

Therefore, the solution to the equation is x = 16/15.